As a manager over a new project with a ridiculous release date, I'm subject to the same political bullshit as everyone else. At this point, I'm of the opinion that anything with a realistic ship date simply won't get funded. So all I do these days is commit to things that I am certain aren't achievable in the time frame on the table, just so that we can get the project off the ground in the first place. From that point, I immediately start to play the game of politics and showmanship to put together a narrative with the usual culprits for why a project is late. Shifting requirements, other teams that didn't deliver what we depended on, etc.
Then I make more promises and estimates, playing the emotional card of "sunk cost" to convince upper management to continue funding the team rather than torpedo the project. Then we ship, and I quickly get everyone on my team promoted "because we shipped" before it becomes clear to upper management that we shipped something essentially worthless to the company. Because we're in a huge profitable company, everyone can jump ship to the next shiny thing, and whoever is left holding the potato on its way to deprecation just gets re-org'd when it gets canned.
I know it's a bullshit game. But I play it well, and all the software developers on my team get paid and promoted because I am so good at it.